Mar. 5 Statistic for the day: U.S. rank, among 102 nations, of perceived corruption (according to Transparency International): 16th least corrupt. Least corrupt: Finland Most corrupt: Bangladesh

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Mar. 5 Statistic for the day U.S. rank, among
102 nations, of perceived corruption (according
to Transparency International) 16th least
corrupt.Least corrupt Finland Most corrupt
Bangladesh
Full list at http//www.transparency.org/cpi/2002/
cpi2002.en.html
Assignment Have a great break
These slides were created by Tom Hettmansperger
and in some cases modified by David Hunter
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Exercise 1, page 309 (sort of)
Suppose you flip four coins.

• Which is more likely, HHHH or HTTH?
• Which is more likely, four total heads or two
  total heads?

Note These questions are not the same! One of
these questions is often mistakenly answered due
to belief in the Law of small numbers (also
known as the Gamblers Fallacy).
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Flip a coin repeatedly. Which of the following
is more likely?

• Your first seven flips are HHTHTTH
• Your first six flips are all heads

(By the way, how do you calculate the exact
probability of each of these events?)
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Exercise 7, page 310

• In a high-risk population, virtually all people
  who test positive will truly be infected, but
  for every infected person correctly identified
  in a low-risk population, an estimated ten
  noncarriers will test positive.
• How can the low-risk statement be true, assuming
  that the test has high sensitivity and
  specificity?

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Exercise 10, page 310
Suppose a rare disease occurs in about 1 out of
1000 people who are like you. A test for the
disease has sensitivity of 95 and specificity of
90. Compute the probability that you actually
have the disease, given that your test results
are positive.
Weve seen several such examples in lecture. A
similar question is pretty much guaranteed on the
midterm!
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Tree diagrams A possible tool for solving
problems like the rare disease problem
All people like you
.001
.999
With disease
Without disease
.05
.95
.10
.90
Positive
Negative
Positive
Negative
.0999
.00095
Pr (Positive) .00095.0999 .10085
Pr (Disease given Positive) .00095/.10085
.0094
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Exercise 15, page 311. Whats the difference
between these two statements?

• Im confident that there is at least one set of
  matching birthdays in this room
• Im confident that there is at least one person
  in this room whose birthday matches my birthday

Which statement is more likely to be true? How
many possible pairs of people are eligible for
matching in each case? Assume 50 people are in
the room.
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With 50 people in the room

• There are 49 possible pairs with me.
• There are 4948471 1225 total possible
  pairs.
• Pr (No match with my birthday) (364/365)49.874
• Pr (No match at all) .030 (and we can estimate
  by (364/365)1225.035)

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Randomized Response A technique for asking
sensitive questions
Question 1 Have you ever smoked
marijuana? Question 2 Is your mothers
birthday in Jan through May? If your fathers
birthday is in July through Dec, answer question
1. Otherwise answer question 2.
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Solve for p .208.5p proportion of yeses
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Stat100 survey Have you ever
smoked marijuana?
marijuana Count Percent No 97
41.45 Yes 137 58.55 N
234 3